In [1]:

    

import numpy as np


    

In [8]:

    

NG = 100
L = 1
x, dx = np.linspace(0, L, NG, retstep=True, endpoint=False)
x


    

    
Out[8]:





array([ 0.  ,  0.01,  0.02,  0.03,  0.04,  0.05,  0.06,  0.07,  0.08,
        0.09,  0.1 ,  0.11,  0.12,  0.13,  0.14,  0.15,  0.16,  0.17,
        0.18,  0.19,  0.2 ,  0.21,  0.22,  0.23,  0.24,  0.25,  0.26,
        0.27,  0.28,  0.29,  0.3 ,  0.31,  0.32,  0.33,  0.34,  0.35,
        0.36,  0.37,  0.38,  0.39,  0.4 ,  0.41,  0.42,  0.43,  0.44,
        0.45,  0.46,  0.47,  0.48,  0.49,  0.5 ,  0.51,  0.52,  0.53,
        0.54,  0.55,  0.56,  0.57,  0.58,  0.59,  0.6 ,  0.61,  0.62,
        0.63,  0.64,  0.65,  0.66,  0.67,  0.68,  0.69,  0.7 ,  0.71,
        0.72,  0.73,  0.74,  0.75,  0.76,  0.77,  0.78,  0.79,  0.8 ,
        0.81,  0.82,  0.83,  0.84,  0.85,  0.86,  0.87,  0.88,  0.89,
        0.9 ,  0.91,  0.92,  0.93,  0.94,  0.95,  0.96,  0.97,  0.98,  0.99])

In [9]:

    

x2 = np.linspace(-dx, L+dx, NG+2, endpoint=False)
x2


    

    
Out[9]:





array([-0.01,  0.  ,  0.01,  0.02,  0.03,  0.04,  0.05,  0.06,  0.07,
        0.08,  0.09,  0.1 ,  0.11,  0.12,  0.13,  0.14,  0.15,  0.16,
        0.17,  0.18,  0.19,  0.2 ,  0.21,  0.22,  0.23,  0.24,  0.25,
        0.26,  0.27,  0.28,  0.29,  0.3 ,  0.31,  0.32,  0.33,  0.34,
        0.35,  0.36,  0.37,  0.38,  0.39,  0.4 ,  0.41,  0.42,  0.43,
        0.44,  0.45,  0.46,  0.47,  0.48,  0.49,  0.5 ,  0.51,  0.52,
        0.53,  0.54,  0.55,  0.56,  0.57,  0.58,  0.59,  0.6 ,  0.61,
        0.62,  0.63,  0.64,  0.65,  0.66,  0.67,  0.68,  0.69,  0.7 ,
        0.71,  0.72,  0.73,  0.74,  0.75,  0.76,  0.77,  0.78,  0.79,
        0.8 ,  0.81,  0.82,  0.83,  0.84,  0.85,  0.86,  0.87,  0.88,
        0.89,  0.9 ,  0.91,  0.92,  0.93,  0.94,  0.95,  0.96,  0.97,
        0.98,  0.99,  1.  ])

In [11]:

    

assert np.allclose(x2[1:-1], x)


    

In [18]:

    

p = np.array(-dx/2)


    

In [20]:

    

(p // dx).astype(int)


    

    
Out[20]:





-1